{"id":"https://openalex.org/W2109402618","doi":"https://doi.org/10.1109/tnn.2008.2005188","title":"Nonlinear Knowledge-Based Classification","display_name":"Nonlinear Knowledge-Based Classification","publication_year":2008,"publication_date":"2008-10-01","ids":{"openalex":"https://openalex.org/W2109402618","doi":"https://doi.org/10.1109/tnn.2008.2005188","mag":"2109402618","pmid":"https://pubmed.ncbi.nlm.nih.gov/18842487"},"language":"en","primary_location":{"id":"doi:10.1109/tnn.2008.2005188","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tnn.2008.2005188","pdf_url":null,"source":{"id":"https://openalex.org/S42080949","display_name":"IEEE Transactions on Neural Networks","issn_l":"1045-9227","issn":["1045-9227","1941-0093"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Neural Networks","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","pubmed"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5033672550","display_name":"O. L. Mangasarian","orcid":null},"institutions":[{"id":"https://openalex.org/I1304256225","display_name":"University of Wisconsin System","ror":"https://ror.org/03ydkyb10","country_code":"US","type":"education","lineage":["https://openalex.org/I1304256225"]},{"id":"https://openalex.org/I135310074","display_name":"University of Wisconsin\u2013Madison","ror":"https://ror.org/01y2jtd41","country_code":"US","type":"education","lineage":["https://openalex.org/I135310074"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"O.L. Mangasarian","raw_affiliation_strings":["Computer Sciences Department, University of Wisconsin, Madison, WI 53706, USA. olvi@cs.wisc.edu","Dept. of Comput. Sci., Wisconsin Univ., Madison, WI"],"affiliations":[{"raw_affiliation_string":"Computer Sciences Department, University of Wisconsin, Madison, WI 53706, USA. olvi@cs.wisc.edu","institution_ids":["https://openalex.org/I135310074"]},{"raw_affiliation_string":"Dept. of Comput. Sci., Wisconsin Univ., Madison, WI","institution_ids":["https://openalex.org/I1304256225"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5065490382","display_name":"Edward W. Wild","orcid":"https://orcid.org/0009-0003-9399-2108"},"institutions":[{"id":"https://openalex.org/I1304256225","display_name":"University of Wisconsin System","ror":"https://ror.org/03ydkyb10","country_code":"US","type":"education","lineage":["https://openalex.org/I1304256225"]},{"id":"https://openalex.org/I135310074","display_name":"University of Wisconsin\u2013Madison","ror":"https://ror.org/01y2jtd41","country_code":"US","type":"education","lineage":["https://openalex.org/I135310074"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"E.W. Wild","raw_affiliation_strings":["Computer Sciences Department, University of Wisconsin, Madison, WI, USA","Dept. of Comput. Sci., Wisconsin Univ., Madison, WI"],"affiliations":[{"raw_affiliation_string":"Computer Sciences Department, University of Wisconsin, Madison, WI, USA","institution_ids":["https://openalex.org/I135310074"]},{"raw_affiliation_string":"Dept. of Comput. Sci., Wisconsin Univ., Madison, WI","institution_ids":["https://openalex.org/I1304256225"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5033672550"],"corresponding_institution_ids":["https://openalex.org/I1304256225","https://openalex.org/I135310074"],"apc_list":null,"apc_paid":null,"fwci":3.7251,"has_fulltext":false,"cited_by_count":58,"citation_normalized_percentile":{"value":0.93100773,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"19","issue":"10","first_page":"1826","last_page":"1832"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10351","display_name":"Liver Disease Diagnosis and Treatment","score":0.9627000093460083,"subfield":{"id":"https://openalex.org/subfields/2713","display_name":"Epidemiology"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}},"topics":[{"id":"https://openalex.org/T10351","display_name":"Liver Disease Diagnosis and Treatment","score":0.9627000093460083,"subfield":{"id":"https://openalex.org/subfields/2713","display_name":"Epidemiology"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}},{"id":"https://openalex.org/T10136","display_name":"Statistical Methods and Inference","score":0.9556999802589417,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.7288834452629089},{"id":"https://openalex.org/keywords/kernel","display_name":"Kernel (algebra)","score":0.6350396871566772},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5349900126457214},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.49452683329582214},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.44295039772987366},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.43429329991340637},{"id":"https://openalex.org/keywords/kernel-method","display_name":"Kernel method","score":0.4222831428050995},{"id":"https://openalex.org/keywords/key","display_name":"Key (lock)","score":0.41094809770584106},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3918033540248871},{"id":"https://openalex.org/keywords/pattern-recognition","display_name":"Pattern recognition (psychology)","score":0.35903093218803406},{"id":"https://openalex.org/keywords/support-vector-machine","display_name":"Support vector machine","score":0.3474521338939667},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3427852988243103},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.3261129856109619},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.1177348792552948}],"concepts":[{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.7288834452629089},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.6350396871566772},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5349900126457214},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.49452683329582214},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.44295039772987366},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.43429329991340637},{"id":"https://openalex.org/C122280245","wikidata":"https://www.wikidata.org/wiki/Q620622","display_name":"Kernel method","level":3,"score":0.4222831428050995},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.41094809770584106},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3918033540248871},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.35903093218803406},{"id":"https://openalex.org/C12267149","wikidata":"https://www.wikidata.org/wiki/Q282453","display_name":"Support vector machine","level":2,"score":0.3474521338939667},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3427852988243103},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.3261129856109619},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.1177348792552948},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[{"descriptor_ui":"D000465","descriptor_name":"Algorithms","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D000465","descriptor_name":"Algorithms","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D000465","descriptor_name":"Algorithms","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D001185","descriptor_name":"Artificial Intelligence","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D001185","descriptor_name":"Artificial Intelligence","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D001185","descriptor_name":"Artificial Intelligence","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D003198","descriptor_name":"Computer Simulation","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D003198","descriptor_name":"Computer Simulation","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D003198","descriptor_name":"Computer Simulation","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D008962","descriptor_name":"Models, Theoretical","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D008962","descriptor_name":"Models, Theoretical","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D008962","descriptor_name":"Models, Theoretical","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D009716","descriptor_name":"Numerical Analysis, Computer-Assisted","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D009716","descriptor_name":"Numerical Analysis, Computer-Assisted","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D009716","descriptor_name":"Numerical Analysis, Computer-Assisted","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D010363","descriptor_name":"Pattern Recognition, Automated","qualifier_ui":"Q000379","qualifier_name":"methods","is_major_topic":false},{"descriptor_ui":"D010363","descriptor_name":"Pattern Recognition, Automated","qualifier_ui":"Q000379","qualifier_name":"methods","is_major_topic":false},{"descriptor_ui":"D010363","descriptor_name":"Pattern Recognition, Automated","qualifier_ui":"Q000379","qualifier_name":"methods","is_major_topic":false},{"descriptor_ui":"D011382","descriptor_name":"Programming, Linear","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D011382","descriptor_name":"Programming, Linear","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D011382","descriptor_name":"Programming, Linear","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D016571","descriptor_name":"Neural Networks, Computer","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D016571","descriptor_name":"Neural Networks, Computer","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D016571","descriptor_name":"Neural Networks, Computer","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D017711","descriptor_name":"Nonlinear Dynamics","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D017711","descriptor_name":"Nonlinear Dynamics","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D017711","descriptor_name":"Nonlinear Dynamics","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true}],"locations_count":3,"locations":[{"id":"doi:10.1109/tnn.2008.2005188","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tnn.2008.2005188","pdf_url":null,"source":{"id":"https://openalex.org/S42080949","display_name":"IEEE Transactions on Neural Networks","issn_l":"1045-9227","issn":["1045-9227","1941-0093"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Neural Networks","raw_type":"journal-article"},{"id":"pmid:18842487","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/18842487","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE transactions on neural networks","raw_type":null},{"id":"pmh:oai:minds.wisconsin.edu:1793/64338","is_oa":false,"landing_page_url":"http://digital.library.wisc.edu/1793/64338","pdf_url":null,"source":{"id":"https://openalex.org/S4306401622","display_name":"Minds at UW (University of Wisconsin)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I135310074","host_organization_name":"University of Wisconsin\u2013Madison","host_organization_lineage":["https://openalex.org/I135310074"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Technical Report"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.4699999988079071,"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":28,"referenced_works":["https://openalex.org/W83112366","https://openalex.org/W85009029","https://openalex.org/W1553407966","https://openalex.org/W1573598582","https://openalex.org/W1574956165","https://openalex.org/W1584120419","https://openalex.org/W1599216479","https://openalex.org/W1601740268","https://openalex.org/W1604938182","https://openalex.org/W1621799579","https://openalex.org/W2032303280","https://openalex.org/W2059890424","https://openalex.org/W2069231281","https://openalex.org/W2093404847","https://openalex.org/W2104260616","https://openalex.org/W2129894900","https://openalex.org/W2156909104","https://openalex.org/W2159737176","https://openalex.org/W2167025280","https://openalex.org/W2171096262","https://openalex.org/W2576490506","https://openalex.org/W2999905431","https://openalex.org/W3120740533","https://openalex.org/W4230674625","https://openalex.org/W4253845129","https://openalex.org/W6603410693","https://openalex.org/W6634814127","https://openalex.org/W6675473091"],"related_works":["https://openalex.org/W2089892314","https://openalex.org/W1603091392","https://openalex.org/W4386075310","https://openalex.org/W2095626363","https://openalex.org/W2169565408","https://openalex.org/W2121506664","https://openalex.org/W2127229869","https://openalex.org/W3123056048","https://openalex.org/W2150638158","https://openalex.org/W2363184354"],"abstract_inverted_index":{"In":[0],"this":[1,43],"brief,":[2],"prior":[3,35,57,104],"knowledge":[4,36,58,105],"over":[5],"general":[6],"nonlinear":[7,12,56,103,108],"sets":[8,95],"is":[9,37,45,75],"incorporated":[10],"into":[11,60],"kernel":[13,90,109],"classification":[14,80],"problems":[15],"as":[16],"linear":[17,21,24,61],"constraints":[18,25],"in":[19,42],"a":[20,46,84],"program.":[22],"These":[23],"are":[26],"imposed":[27],"at":[28],"arbitrary":[29],"points,":[30],"not":[31,113],"necessarily":[32],"where":[33],"the":[34,49,64,72,100],"given.":[38],"The":[39],"key":[40],"tool":[41],"incorporation":[44],"theorem":[47],"of":[48,71,102],"alternative":[50],"for":[51,92],"convex":[52],"functions":[53],"that":[54,111],"converts":[55],"implications":[59],"inequalities":[62],"without":[63],"need":[65],"to":[66,107],"kernelize":[67],"these":[68,93],"implications.":[69],"Effectiveness":[70],"proposed":[73],"formulation":[74],"demonstrated":[76],"on":[77],"publicly":[78],"available":[79],"data":[81,87,94],"sets,":[82],"including":[83],"cancer":[85],"prognosis":[86],"set.":[88],"Nonlinear":[89],"classifiers":[91,110],"exhibit":[96],"marked":[97],"improvements":[98],"upon":[99],"introduction":[101],"compared":[106],"do":[112],"utilize":[114],"such":[115],"knowledge.":[116]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":3},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":10},{"year":2012,"cited_by_count":2}],"updated_date":"2026-01-13T01:12:25.745995","created_date":"2025-10-10T00:00:00"}